Trading Strategies for Cryptocurrencies:

Are Technical Indicators Useful for Trading Cryptocurrencies?

IS713: Foundations for Data Analytics 18 November 2021

CHIN Joo Ern (jooern.chin.2020@msc.smu.edu.sg) LOH Yi Lin (yilin.loh.2021@msc.smu.edu.sg)

LU Yu Xiao (yxlu.2021@phdcs.smu.edu.sg) YANG Chengran (cryang.2021@phdcs.smu.edu.sg) YANG Zhou (zhouyang.2021@phdcs.smu.edu.sg)

1. Introduction

   In today’s fast paced and constantly growing world, inflation has become a constant reality that constantly depreciates the value of money. Inflation is borne from three key drivers:

   1. Excess aggregate demand over supply from a consumerist world.

   2. Cost-push effects resulting from monopolies and oligopolies in different markets, rising unit labor cost, diminishing supply of raw materials for production and transport, increasingly unpredictable and extreme weather.

   3. The autoregressive cycles of economic expansion and contraction through socio-political intervention by governing bodies and unions in the form of revisions of prices, wages and rents that manipulate inflation according to their market objectives[2]. Relying on wage increments alone and bank interest rates to cope with inflation is no longer a feasible strategy in most contexts and the global population has noticed this, resulting in a rise in retail trading as a tool for the average working adult to ensure their money keeps abreast with growing prices[3].

   To reduce the effects of inflation, many take to investment in order to increase their capital [18]. Traditional forms of investment [19] can include equities, commodities, and bonds among many others. Furthermore, depending on the risk appetite, traders can adopt many different strategies, from long term fundamental based trading to day-trading, or even leveraged trading.

   There are many mechanisms which a trader can use to invest to grow their money. Most commonly, the direct buying and selling of an instrument is used. When a trader believes that the value of an instrument - foreign currency exchange, equities, or commodities - is undervalued and expects the price to increase, a buy order is made at the current price in anticipation that the price will increase. This is known as a ‘long’ order. Conversely, when the price of an instrument is expected to drop, a trader will make a sell order, effectively borrowing a stock at the current price with the intention of buying it later at a lower price. The decision as to whether a price is expected to rise, or fall, can be based on either fundamental analysis, technical analysis or intuition and experience. Fundamental analysis, as earlier discussed, focusses on the company’s presumed fundamental value. In contrast, technical analysis typically uses the movements, patterns, and history of prices to make trading decisions. The tools and systems which a trader uses to analyze the movements and history of prices and make trading decisions is known as their trading strategy.

   In recent years, the introduction of Bitcoin [1] in 2009, has led to the creation of a new market, the cryptocurrency market. This market has seen huge adoption and interest from the public, with thousands of cryptocurrencies available for traders to trade and an overall market capitalization in the trillions of dollars. The price of Bitcoin has also risen exponentially since its inception, and many people have earnt a fortune – and an unlucky few have lost their life savings – betting on Bitcoin. Although Bitcoin has seen an exponential price increase, there has been several waves in the Bitcoin market so far, with the bitcoin market gaining – and losing up to a trillion dollar in market value within the course of a week. Bitcoin prices do not move like the stock market, it is

   more volatile and driven by events and investor sentiment. In fact, many have likened Bitcoins to bubbles in the stock market, where prices increase rapidly due to speculative investment, followed by a crash where sell-offs cause the price to decline dramatically, leaving speculative investors in the lurch.

   While the less informed trader might simply follow market hype when entering the Bitcoin market, some more informed investors have taken to using various methods to try and gain profits from trading Bitcoin or other cryptocurrencies. Among those methods is the use of technical analysis in predicting future cryptocurrency prices. The goal of this paper is thus to examine whether technical indicators are useful for trading in the Cryptocurrency Market.

   A brief introduction to the technical indicators that are used for the technical analysis and trading strategies is provided to better understand the application of these indicators for making trading decisions (see Annex A). The selected indicators and their corresponding trading strategies are some of the most used indicators that are accessible and understood by most traders. This was intentionally done to ensure the impact of the conclusion affects as many traders as possible.

   The structure of the paper is as follows: Section 2 briefly discusses how the data was sourced and the processing done to generate the final dataset. Section 3 fits the data to various Autoregressive Distributed Lag (ADL) time series models to determine (i) the variables that are strongly correlated profitable trades, (ii) the lag intervals for specific variables which result in the highest correlation, and (iii) potentially useful interaction terms that indicate marginal increases in trading success conditioned on specific variable states. In Section 4, we dive deep into robustness checks by applying a different time series model (ECM) to determine if previously significant indicators remain so, or if other significant indicators are found. Following which, in Section 5, a full trading strategy is developed based on the insights derived from the earlier models, and this strategy is evaluated against common trading strategies on a different cryptocurrency from the one used in the earlier models to determine its relative performance. Finally, in Section 6, the paper concludes with a summary of the findings and potential improvements that can be made for both the modelling and trading strategy.

   BTC-USD (the price of Bitcoin in USD) will be used as the base market for modelling since it is the largest and most popular cryptocurrency. The decision to explore this specific market using technical analysis is because technical analysis is the most quantitative method used to make trading decisions, making it a prime candidate for the application of econometric analysis. Additionally, cryptocurrencies are a nascent market whose true fundamentals have not been established, making fundamental analysis extremely difficult and likely inaccurate. Lastly, Bitcoin’s price is highly susceptible to news-induced price action (be it news with a known release date, or sudden news), this makes it a unique challenge for regressive models as the trend is not fixed nor cyclical.

2. Data Collection and Processing

   Market data collected for this project is largely from Yahoo! finance and WSJ markets website. All data is collected on the daily timeframe for the past 5 years. Aside from that, the data used to represent new-based hype for markets is collected from Google Trends by searching for key words, and significant events affecting the Bitcoin market are included as control variables. Market indicators are generated using the TA-Lib Python library, while the common strategies used to apply the market indicators to make trades are consolidated and coded based on information from Investopedia and Wysetrade.

   During the implementation of the strategy, trades made by the strategy were thoroughly checked through visualization and comparison

   
   

   Figure 1. BTC (2018-2020) RSI Strategy Visualized

   against the conditions for making each trade (example seen in Figure 1.). The actions were then plotted against actual market conditions to determine if the strategy was performing as intended. Buy orders are coded as ‘1’ and sell orders are coded as ‘-1’, while a state of ‘0’ indicates that the specific strategy does not recommend making a trade given the conditions. The different variables and their definitions are as follows:

   • Future_Price(x) % Profit/Loss – The percentage difference in price of the asset x days from the given date.

   • Close – The closing price of an instrument on a given date.

   • Volume – The number of trades made for an instrument on a given date.

   • RSI – The Relative Strength Index of that instrument on a given date.

   • RSI Condition – The trades made by the RSI based strategy on a given date, when RSI is above 70, a sell trade is made because the instrument is considered to be overbought, when RSI is below 30 a buy trade is made because the instrument is considered to be oversold.

   • MACD Condition – The trades made by the MACD strategy on a given date, when the MACD line crosses the Signal line from above, a sell trade is made because the shorter term up trend has reversed and caught up with the price of longer-term

   • EMA - When the MACD line crosses the Signal line from below, the reverse applies and a buy trade is made.

   • EMA Condition – The trades made by the EMA strategy on a given date, when the price is above the 25EMA, 50EMA, 100EMA and 200EMA, both the short, middle and longterm trend is positive and a buy order is made, when the price is below all aforementioned EMAs, the reverse applies and a sell order is made.

   • Close-EMA200 Price Diff – The difference in price between the closing price and EMA200 on a given date.

   • Bollinger Band Condition – The trades made by the Bollinger Band strategy on a given date, when the price touches the upper band, a sell order is made, while a buy order is made when the price touches the lower band.

   • ATR – The Average True Range on a given date, it is used as a control variable for volatility.

   • Trend – Takes a value of ‘1’ to represent an uptrend when the price is above the 200EMA and takes a value of ‘-1’ to represent a downtrend when price is below the 200EMA.

   • Forecasted % Profit – A projection of a linear regression done on the past 14 days to estimate the future price on the next day, it is converted into a percentage by the following

     equation: 𝐹𝑜𝑟𝑒𝑐𝑎𝑠𝑡𝑒𝑑 𝑃𝑟𝑖𝑐𝑒−𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝑃𝑟𝑖𝑐𝑒

     𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝑃𝑟𝑖𝑐𝑒

     
     

   • Slope – The gradient of the 14-day regression line used in Forecasted % Profit.

   • Acceleration – The rate of change of Slope.

   • Certain modifiers are applied to the variables, including

     • Price Relative – which indicates that the variable is divided by the closing price

     • Log() – which indicates that the log function is applied to the variable.

     • Interaction Terms - Lastly, if an x is seen in the variable name like A x B, it indicates that it is an interaction term between variable A and B.

   
   

3. Main Models

   To derive insights regarding the correlation between the different independent variables and the expected profit from the time series data whilst factoring in additional exogenous factors, an autoregressive distributed lag (ADL) [14] model was used to model the BTC-USD data from 4/4/2015 – 15/4/2020. ADL modelling allows for several different parameters to adjust the based on the context of the problem. These parameters capture (i) whether the relationship between the exogenous and endogenous variables are causal, (ii) the different lags for each variable, and (iii) whether the type of trend the data exhibits.

   One key assumption that threatens the validity of the ADL model in this context is stationarity. However, since the data is collected across a relatively short time (5 years), the stationarity

   concerns are not considered to be entirely relevant since the true characteristics of the dataset are still considered to be in flux. Assumptions regarding the true lag length of the model can be further studied but are not considered in this research as we work with only the most data (lag=1) under the assumption that market conditions change quickly and increasing the lag tends to result in increased noise. Large outliers and multicollinearity within regressors were checked for using the Python statsmodels library and found to be absent.

   Additionally, non-linear terms were added to capture potential non-linear relationships, while interaction terms were added to capture the marginal effects that one variable has, conditioned on the state of another variable.

   1. Base Autoregressive Distributed Lag Model

      The basic ADL model allows for k additional predictors, with q1 lags of the first predictor are included along with qi lags of the ith predictor takes the following form:

      𝒀𝒕 = 𝜷𝟎 + 𝜷𝟏 𝒀𝒕−𝟏 + 𝜷𝟐 𝒀𝒕−𝟐 + ⋯ + 𝜷𝒑 𝒀𝒕−𝒑 + 𝜹𝟏𝟏𝑿𝟏𝒕−𝟏 + 𝜹𝟏𝟐𝑿𝟏𝒕−𝟐 + ⋯ +𝜹𝟏𝒒𝟏 𝑿𝟏𝒕−𝒒𝟏 + ⋯

      + 𝜹𝒌𝟏𝑿𝒌𝒕−𝟏 + 𝜹𝒌𝟐𝑿𝒌𝒕−𝟐 + ⋯ + 𝜹𝒌𝒒𝒌 𝑿𝒌𝒕−𝒒𝒌 + 𝒖𝒕

      
      

      Predictors used include 'Close', 'Volume', ' RSI', 'RSI Condition', 'MACD Condition' 'EMA Condition', 'Close-EMA200 Price Diff', 'BB Condition', ' ATR', 'Trend', 'Forecasted', 'Slope' and 'Acceleration', all of which have been defined in Section 2. The lags applied for all predictors and endogenous variables is kept constant within each model for simplicity, although this can be adjusted to better fit the ADL model to the predictors. The performance of each model is captured by both the log-likelihood of the model and the mean squared forecast error final prediction error (MSFEFPE) which is given by the following equation:

      
      

      T = Number of observations, p = Number of lag periods applied SSR = Sum squared residual between predicted and actual values

      
      

      Results from Table 2. show that assuming the predictors have a causal relationship to the dependent variable decreases the goodness of fit of the model as seen from the higher log-likelihood score, but also decreases the MSFE [15] which indicates that the prediction is more accurate. The causal parameter removes the lags that begin at 0 and only uses predictors lagged by a period of 1 or more. Considering that certain trading signals such as the MACD and RSI [16] can be extremely time sensitive as they use a swing trading strategy and trade at the point of price reversals, lagging these predictors would cause the timing of the reversals to be off. However, it is also important to realize that due to the general effect of having a lower number of predictors when a causal relationship between exogenous and endogenous variables is assumed, the model’s decrease in goodness of fit could be simply due to it having significantly fewer predictors as compared to the

      model where the causal relationship is not assumed. We tested this assumption and found that the difference in performance is equally pronounced between models with a lag of 1 as compared to models with a lag of 5, indicating that the predictors with a time lag of 0 are equally important in fitting the models with different lags, but in doing so, also causes MSFE to increase. Considering that the conditions in which a trade is made does not a strictly causal relationship with the trade profitability, we decided to proceed with no assumption of a causal relationship.

      
      

      Table 2: ADL Model Comparison (Causal Parameter)
      Model	AR(1)-BH(1)	AR(1)-BH(1)	AR(5)-BH(1)	AR(5)-BH(1)
      Causal	False	True	False	True
      Log Likelihood	3397.9	3359.0	3441.0	3401.9
      MSFEFPE	0.001388	0.001346	0.001445	0.001408

      AR(x) indicates that x periods of lag are applied to the variables

      BH(y) indicates that the profit is based on a trade closed after holding for y days

      
      

      ADL models are also able to capture trend effects through additional trend parameters. Table 3. captures the different performances of the model under different trend assumptions. Due to the volatility of the BTC-USD market, we expect that there might not be a clear trend. Although it can be said that there is a general overall upward trend with fluctuations in trend for specific periods of time, this is not easily captured by a constant or second order trend across time. This limits the applicability of trend effects captured by the model using the ∂itj parameters, where j=0 indicates that there is no trend, j=1 indicates a constant trend and j=2 indicates a time trend. The model’s form is rewritten as follows to capture trend effects:

      𝒀𝒕 = 𝝏𝟎 + 𝝏𝟏𝒕 + 𝝏𝟐𝒕𝟐 + 𝜷𝟎 + 𝜷𝟏 𝒀𝒕−𝟏 + 𝜷𝟐 𝒀𝒕−𝟐 + ⋯ + 𝜷𝒑 𝒀𝒕−𝒑 + 𝜹𝟏𝟏𝑿𝟏𝒕−𝟏 + 𝜹𝟏𝟐𝑿𝟏𝒕−𝟐

      + ⋯ +𝜹𝟏𝒒𝟏 𝑿𝟏𝒕−𝒒𝟏 + ⋯ + 𝜹𝒌𝟏𝑿𝒌𝒕−𝟏 + 𝜹𝒌𝟐𝑿𝒌𝒕−𝟐 + ⋯ + 𝜹𝒌𝒒𝒌 𝑿𝒌𝒕−𝒒𝒌 + 𝒖𝒕

      Table 3: ADL Model Comparison (Trend Parameter)
      Model	AR(1)-BH(1)	AR(1)-BH(1)	AR(1)-BH(1)	AR(1)-BH(1)
      Trend	Constant	No Trend	Time Trend	Constant and Time Trend
      Log Likelihood	3397.9	3395.7	3399.6	3402.3
      MSFEFPE	0.001388	0.001386	0.001397	0.001399

      The results show that there is a small increase in fit, but also an increase in MSFE when trend terms are added to the model. Hence, considering that based on the understanding of the USDBTC market being a highly volatile environment, we will work with the assumption that there is no trend in the time series model.

   2. Variable Modification

      Having established that the model’s general structure works when (i) assuming a causal relationship between endogenous and exogenous variable, and (ii) having no trend, we proceeded to determine the effects of modifying specific parameters and adding non-linear terms and interaction terms to augment the model. This effort was conducted because the exact relationship between the predictors and the dependent variable is not easily reasoned out for the context of the problem. Price movement is a complex variable that is partly governed by social factors (an agglomeration of decisions made by individuals and institutions) as opposed to mathematical patterns. Numerous researchers have also explored the possibility that price movements can in fact be approximated by using the sentiment of the population as the main predictor [5] and we conduct similar studies in later sections of the paper where we factor in market hype into the model using Google Trends. However, in this section, we work on different variations of the existing predictors to improve the accuracy of the model and discuss the effects of other factors in subsequent sections.

      Firstly, we changed the Forecasted variable to Forecasted % Profit, which we felt is more relevant considering the dependent variable is a function of the percentage profit. Aside from that, we also corrected the ATR control variable to become Price Relative ATR. Since the ATR is affected by the price, the market would appear to be more volatile when the asset is worth a larger price if is not demeaned by the price. This was similarly done for Volume although in this context, the correction is partial. Volume of trades in Bitcoin increases steadily over time, but in this model, it is being used as a control variable for the market activity. Since there were fewer traders of Bitcoin in its early stages, the volume of trades required for the market to be considered active in that period should be smaller. We corrected the market activity with the general popularity of Bitcoin, which is a function of the price, revising it to become Price Relative Volume. Lastly, we applied the same logic to Close-EMA200 Price Diff and revised it to become Price Relative Close-EMA200 Price Diff which captures the deviation from the exponential moving average relative to the magnitude of the price. We found that by making these adjustments, the variable’s coefficients all increased, indicating that the significance they have on the model has increased. Most notably we noted that the Close-EMA200 Price Diff becomes statistically significant at the 1% level of significance when this modification is made. The net effects to the model fit and performance is captured in Table 4. while the changes to the variable’s coefficients and statistical significance are captured in Table 5.

      
      

      Table 4: ADL Model Comparison (Effects of Modification of Terms)
      Model	AR(1)-BH(1) Pre-Modified	AR(1)-BH(1) Post-Modified
      Causal	False	False
      Trend	No Trend	No Trend
      MSFEFPE	0.001392	0.001401

      
      

      Table 5. Effects of Modification of Terms
      Pre-Modified Variable	Pre-Modified Coefficient	Pre-Modifie d P>|z|	Post-Modified Variable	Post-Modified Coefficie nt	Post-Modifie d P>|z|
      Volume.L0	-3.77E-13	0.358	Price Relative Volume.L0	-1.59E-10	0.955
      Volume.L1	3.12E-13	0.435	Price Relative Volume.L1	8.22E-10	0.765
      Close-EMA200 Price Diff.L0	0.0009	0.477	Price Relative Close-EMA200 Price Diff.L0	-0.2212	0.001***
      Close-EMA200 Price Diff.L1	-0.0009	0.476	Price Relative Close-EMA200 Price Diff.L1	0.2141	0.001***
      ATR.L0	0.0001	0.082	Price Relative ATR.L0	0.0051	0.176
      ATR.L1	-9.33E-05	0.119	Price Relative ATR.L1	-0.0039	0.295
      Forecasted.L0	0.0001	0.507	Forecasted % Profit.L0	-0.0575	0.579
      Forecasted.L1	-0.0001	0.527	Forecasted % Profit.L1	0.0845	0.354

      * = significant at 10%, ** = significant at 5%, *** = significant at 1%

   3. Non-Linear Terms

      Following the term modifications, non-linear terms [17] were also added to the model to capture potential non-linear relationships between variables. Price Relative Volume, Price Relative Close-EMA200 Price Diff and Price Relative ATR were identified as variables that may have a non-linear relationship with profit, specifically, it is suspected that the effects of market activity, deviation from mean and price volatility has a decreasing level of impact as their magnitudes increase, suggesting a possible log-linear relationship with profit levels. While Log(Price Relative Volume) and Log(Price Relative ATR) may be generated by applying the logarithmic function to the variables directly, due to the negative values in Price Relative Close-EMA200 Price Diff it is necessary to first convert the values to positive floats with a value greater than 1 before applying the logarithmic function and reinstating the original signs to the floats. Table 6 shows the performance of the models with different non-linear term combinations.

      
      

      Table 6. ADL Model Comparison (Effects of Non-Linear Terms)
      Model	AR(1)-BH(1)	AR(1)-BH(1)	AR(1)-BH(1)
      Replaced Non-linear Terms	None	log(Price Relative Volume)	log(Price Relative Volume) log(Price Relative ATR log(Price Relative Close-EMA200 Price Diff)
      Log Likelihood	3404.5	3405.2	3399.6
      MSFEFPE	0.001401	0.001401	0.1400

      
      

      Table 7. Effects of Non-linear Terms
      Pre-Modified Variable	Pre-Modified Coefficient	Pre-Modifie d P>|z|	Post-Modified Variable	Post-Modified Coefficien t	Post-Modifie d P>|z|
      Price Relative Volume.L0	-1.59E-10	0.955	log(Price Relative Volume).L0	0.0025	0.482
      Price Relative Volume.L1	8.22E-10	0.765	log(Price Relative Volume).L1	-0.0032	0.355
      Price Relative Close-EMA200 Price Diff.L0	-0.2212	0.001***	log(Price Relative Close- EMA200 Price Diff).L0	-0.3833	0.009***
      Price Relatively Close-EMA200 Price Diff.L1	0.2141	0.001***	log(Price Relative Close-EMA200 Price Diff).L1	0.3539	0.015**
      Price Relative ATR.L0	0.0051	0.176	log(Price Relative ATR).L0	0.0174	0.338
      Price Relative ATR.L1	-0.0039	0.295	log(Price Relative ATR).L1	-0.0132	0.467

      * = significant at 10%, ** = significant at 5%, *** = significant at 1%

      As seen in Table 7. the log-linear relationship between Price Relative Volume and expected profits holds as the statistical significance of the variable increases. However, the same cannot be said for Price Relative Close-EMA200 Price Diff and Price Relative ATR. Hence the model will

      only be adjusted to include an additional Log(Price Relative Volume) term to capture this potential non-linear relationship with the percentage profits.

   4. Interaction Terms

      Table 8: ADL Model Comparison (Effects of Interaction Terms)
      Model	AR(1)-BH(1)	AR(1)-BH(1)
      Interaction Terms	Absent	Present
      Log Likelihood	3405.2	3409.7
      MSFEFPE	0.001401	0.001400

      Interaction terms are useful for determining if the marginal effects of a variable conditioned on another variable are significant. Typically, we would expect that the signal-based indicators that make swing trades tend to perform better when the direction of the trade is following the trend, so we added interaction terms for all possible combinations of swing trade indicator variables, and conditioned them on both the Trend and the Price Relative Close-EMA200 Price Diff. The log likelihood of the model increases while the MSFE decreases minimally, indicating that the interaction terms do indeed contribute to the model performance. Table 8. shows the performance of the model with and without the interaction terms and Table 9. shows the coefficients and statistical significance of the interaction terms. While it is noted that the interaction terms are all not statistically significant at

      the 10% level of significance, the improvements across both the log likelihood and MFSE suggest it is beneficial to keep the terms for the model.

      
      

      
      

      Table 9. Interaction Term Coefficients and Statistical Significance
      	Coefficient	P>|z|
      RSI x Trend.L0	-0.0003	0.33
      RSI x Trend.L1	0.0001	0.58
      RSI x Price Relative Close-EMA200 Price Diff.L0	0.0015	0.33
      RSI x Price Relative Close-EMA200 Price Diff.L1	-0.0017	0.22
      RSI Condition x Trend.L0	-0.0002	0.97
      RSI Condition x Trend.L1	-0.0062	0.37
      RSI Condition x Price Relative Close-EMA200 Price Diff.L0	-0.0099	0.64
      RSI Condition x Price Relative Close-EMA200 Price Diff.L1	0.002	0.93
      MACD Condition x Trend.L0	-0.0016	0.8
      MACD Condition x Trend.L1	0.0031	0.63
      MACD Condition x Price Relative Close-EMA200 Price Diff.L0	0.0156	0.49
      MACD Condition x Price Relative Close-EMA200 Price Diff.L1	-0.0086	0.7

   5. Determining Optimum Lag

      Previous sections have identified which regressors are statistically significant in the model, however the optimal number of lags to be applied for the model have yet to be determined. By using Bayes’ Information Criteria (BIC) and Akaike’s Information Criteria (AIC), we can assess a model’s goodness-of-fit at different lags. BIC and AIC are given by the following formula:

      
      

      
      

      T = Number of observations, p = Number of lag periods applied SSR = Sum squared residual between predicted and actual values

      
      

      The lags tested range from 1-10 and we found that the lag which gives the most negative BIC and AIC is the lag of 1. AIC favors having more lags as it reduces the effects of the number of observations by having a constant second term. Both criteria balance between the model-fit and regressor coefficients. Model performance for the different lags is shown in Table 10. below:

      
      

      Table 10. Model Fit at Different Lags
      Model Lag / Performance	Lag = 1	Lag = 2	Lag = 4	Lag = 6	Lag = 8	Lag = 10
      BIC	-6577	-6478	-6327	-6159	-5965	-5827
      AIC	-6738	-6715	-6718	-6705	-6665	-6681

      
      

      Considering that the ADL model contains lags for each indicator, yet each indicator has different lags for price impact, we set different lags for the ADL model for comparison and found that RSI, MACD Condition and Price Relative Close-EMA200 Price were statistically significant across different models. Moreover, the MSFEFPE decreases with increase of the lag. This is probably because ADL with lag = 10 has more parameters, so the model can better fit the function between indicator and price. However, the highest statistical significance for lag varies from indicator to indicator as seen in Table 11.

      For RSI indicator, when the lag range is extended, RSI.L9 and RSI.L10 increases in statistical significance compared with RSI.L0 and RSI.L1. The RSI indicator is based on the principle of supply and demand equilibrium, by measuring the total increase in stock prices in a certain period as a percentage of the past 14-day average of the total change in stock prices, RSI assesses the strength of long and short forces, and then suggests specific operations. Based on the above facts, RSI only describes momentum and does not directly give a suggestion to buy or sell

      but should be combined with other indicators to make a proper trading decision, so it is understandable that RSI is statistically significant with a larger lag as it relies on trend change (which is slower) in response to the change in momentum.

      For MACD Condition indicator, when the lag range is extended, MACD Condition.L0 and MACD Condition.L4 become most statistically significant. MACD is a technical indicator that uses the convergence and divergence between the short-term (12-day) exponential moving average and the long-term (26-day) exponential moving average of the closing price to make a judgment on the timing of buying and selling. Because MACD signals the instant of buying or selling, the MACD Condition.L0 having the highest statistical significance across all MACD lag terms is not surprising.

      Table 11. Highest Statistical Significance for Terms at Different Lags
      ADL-Lag1	Coeff	P>|z|	ADL-Lag5	Coefficien t	P>|z|	ADL-Lag10	Coeff	P>|z|
      RSI.L0	0.0012	0.015 **	RSI.L0	0.0014	0.009 ***	RSI.L9	0.0018	0.011 **
      RSI.L1	-0.0009	0.050 **	RSI.L1	-0.0013	0.060 *	RSI.L10	-0.0018	0.001 ***
      Price Relative Close-EMA200 Price Diff.L0	-0.1575	0.119	Price Relative Close-EMA200 Price Diff.L1	0.5211	0.003 ***	Price Relative Close-EMA200 Price Diff.L2	-0.5403	0.005 ***
      Price Relative Close-EMA200 Price Diff.L1	0.1625	0.118	Price Relative Close-EMA200 Price Diff.L2	-0.5788	0.001 ***	Price Relative Close-EMA200 Price Diff.L10	0.3985	0.003 ***
      MACD Condition.L0	0.0254	0.000 ***	MACD Condition.L4	0.0107	0.011 **	MACD Condition.L0	0.0283	0.000 ***
      MACD Condition.L1	0.0006	0.888	Price Relative Close-EMA200 Price Diff.L3	0.4786	0.006 ***	MACD Condition.L4	0.0109	0.017 **

      * = significant at 10%, ** = significant at 5%, *** = significant at 1%

   6. Results and Conclusions

      Based on all the models above, we noted that the RSI, MACD Condition and Price Relative Close-EMA200 Price Diff were consistently statistically significant across most of the models. This indicates that these variables are likely to play a critical role in determining the profitability of a trade and will be useful in the development of a more advanced trading strategy that outperforms the basic strategies. Additionally, we noted that the lag of 1 is most suitable for our model, producing the highest BIC and AIC score between lags 1-10.

      
      

4. Robustness Checks

   In addition to the model robustness checks conducted via variable modification, additional non-linear and interaction terms and testing the model with different lags, further checks were conducted to ascertain the significance of the regressors. One of the key methods used is the

   exploration of additional control variables based on hypothesis. The two key hypotheses are (i) market hype affects the trading price of Bitcoin and (ii) major events can affect the trading price of Bitcoin are explored in Section 4.1 - 4.2 and fully detailed in Annex B. We also conducted a different form of robustness checks by fitting the data to an ECM to determine if the results are statistically significant which will be discussed in Section 4.3.

   1. Market Hype - Google Trends

      Researchers have conducted empirical studies [6,7,8,9] to demonstrate that the investors may have a "herd mentality" when making investment decisions, i.e., other investors' actions may affect one investor's own decision. For example, if one investor finds that many people (e.g., their friends) on the Internet are discussing cryptocurrency, they are more likely to start investing in cryptocurrency.

      In the current society where social media is well-developed, retail investors are not only affected by people around them (e.g., friends or colleagues). They also receive instant information from the Internet or social media. Suppose investors see that people on the Internet are all talking about Bitcoin. In that case, they may not be able to resist the temptation to search Bitcoin and seek potential investment opportunities. Google is currently one of the most widely used search engines in most of the countries in the world. Google trends are some aggregated data showing that how frequently Google users search certain keywords. Such data can be used to understand and predict financial [10] and even public health events [11]. For example, researchers use the abnormal increase of Google search trends of keywords like "headache", "cough", etc., to estimate whether Covid-19 has been spread in certain regions [1].

      In this section, we plan to analyze whether Google Trends data can help our model perform the changes in Bitcoin price. The following two intuitions motivate us to perform such an analysis. On the one hand, Google Trends, to some extent, can reflect the new investors into the cryptocurrency market. A surge in the frequency of a cryptocurrency-related keyword being searched can mean that more investors are paying attention to it, and as a result, they may eventually become investors, which leads to a rise in the Bitcoin price. On the other side, Google Trends may reflect some important events in cryptocurrency investments. An example would be, big companies announcing that they accept Bitcoin for payment or the reward for mining bitcoin transactions is cut in half (Bitcoin halving events).

      After pre-processing these weekly data into daily data, we add the Google Trends data as an additional independent variable and got the following statistical results related to the Google Trend as shown in the Table 12.:

      
      

      Table 12. Statistical Significance of Google Trends
      Variable	Coeff	Std err	z	p > |z|	[0.025	0.975]
      GTrend-L0	0.0002	0.001	0.288	0.773	-0.001	0.001
      GTrend-L1	0.00017	0.001	0.033	0.974	-0.0001	0.001

      As we can observe from Table 12, the significance for both trend-L0 and trend-L1 is not high, which means that the Google Trend data on “Bitcoin” does not contribute to making a better model. Based on the analysis of using Google Trend as an additional independent variable, we conclude that there is no strong evidence suggesting the strong correlation between Google Trend data and the Bitcoin price change.

   2. Major Events – Bitcoin Upgrade (SegWit) and Halving

      Since Bitcoin was introduced in 2009, it has gone through several bull runs – in 2011, 2013, 2017 and, in 2021, is currently going through another. The meteoric increase in prices during Bitcoin’s bull runs have garnered Bitcoin a huge amount of interest from the public and have most commonly been attributed to an upgrade of Bitcoin’s technology, and the halving of rewards for Bitcoin miners. From the table below, it can clearly be seen that there is some sort of correlation between Bitcoin’s bull runs and the halving dates/bitcoin upgrade.

      
      

      Bitcoin Upgrade	Halving Dates	Bitcoin Bull Runs
      		2011
      15 May 2013	November 2012	2013
      24 August 2017	9 July 2016	2017
      November 2021	May 2020	2021

      
      

      In this section, we use the 2017 Bitcoin upgrade (SegWit) as a control variable to determine its statistical impact on the price of Bitcoin and Future_Price(x) % Profit/Loss, as described in Section 3. First, by using a dummy variable to run ARDL, the results show that the event is not statistically significant when regressed on Future_Price(x) % Profit/Loss. Additionally, running ARDL on different time frames show that the event becomes even less statistically significant as the as time frame increases.

      
      

      ARDL REGRESSION TABLE
      VARIABLE	Coeff	Std err	z	p > |z|	[0.025	0.975]
      Segwit.L0	56.5812	298.567	0.190	0.850	-528.989	642.151
      Segwit.L1	59.2099	299.140	0.198	0.843	-527.485	645.905

      
      

      Next, performing the Chow test on Bitcoin’s Close price to USD and the SegWit event dummy variable, yields a Chow score of 0.053 and a p-value of 1.68e-12, which is statistically significant. This also matches with what is seen on the BTC-USD chart, where the trend in Bitcoin prices after the SegWit event was much steeper than before the event. Performing the Chow test on Future_Price(1) % P/L to Close price and the SegWit event yields a p-value of 0.00029, which is statistically significant. However, Performing the Chow test on Future_Price(3) % P/L yields a p-value that is not statistically significant. Additionally performing ARDL regression on the dummy variables with each of the indicators give a statistically insignificant p-value and performing the Chow test on all mentioned indicators give a statistically insignificant result.

      This shows that there is a significant trend change in Future_Price(1) % P/L as compared to Close price upon the SegWit event occurring, however, the trend change becomes insignificant as a result of the structural break if the projection of Future_Price(x) % P/L were to be increased. The structural break also does not affect the effect of technical indicators on future prices. Running the Chow test on the 2016 Bitcoin reward halving produces similar results, with a statistically significant p-value of 0.0035 for BTC-USD price, and 1.32e-18 for Future Price(1)-Close price. Similarly, using the dummy variable directly for ARDL regression produces statistically insignificant results.

      
      

   3. Error Correction Model (ECM)

      For unstable time series, it can be transformed into a stable series by difference method, and a classic regression analysis model can be established. For example, we may establish a regression model between per capita consumption level (Y) and per capita disposable income (X):

      𝑌𝑡 = 𝛼0 + 𝛼1X𝑡 + 𝜇𝑡

      If Y and X have a common upward or downward trend, then we can differentiate X and Y so that they will become a stationary series, and the difference regression model is established:

      𝛥𝑌𝑡 = 𝛼1𝛥X𝑡 + 𝑣𝑡 𝑤ℎ𝑒𝑟𝑒 𝑣𝑡 = 𝜇𝑡 − 𝜇𝑡−1

      However, this approach will cause two problems: (1) If there is a long-term stable equilibrium relationship between X and Y, 𝑌𝑡 = α0 + α1X𝑡 + 𝜇𝑡, but there is no serial correlation in the term

      𝜇𝑡. Then 𝑣𝑡 in the differential formula 𝑌𝑡 = 𝛼0 + 𝛼1X𝑡 + 𝜇𝑡 is a first order moving average time series, so it is serially correlated; (2) If the estimation is done in differential form, important information about the level values of the variables will be ignored, when the model only expresses the short-run relationship between X and Y, but does not reveal the long-run relationship between them. This is because from a long-run equilibrium point of view, the change in Y in period t depends not only on the change in X itself, but also on the state of X and Y at the end of period t-1 and on the degree of imbalance between X and Y in period t-1. Also, the use of differential variables tends to yield unsatisfactory regression equations.

      For example, when using the 𝛥𝑌𝑡 = α1𝛥X𝑡 + 𝑣𝑡 regression, it is rare that the intercept term is significantly zero, i.e., we often obtain an equation of the following form:

      𝛥𝑌𝑡 = 𝛼̂0 + 𝛼̂1𝛥X𝑡 + 𝑣𝑡 𝛼̂0 ≠ 0 (1)

      With X held constant, Y will also keep its long-run equilibrium value constant if the model has a static equilibrium (static equilibrium). However, if we use equation (1), Y will be in a long-run up or down process even if X remains constant, which means that there is no static equilibrium between X and Y. This is inconsistent with most economic theory hypotheses that have static equilibrium. Hence the error correction models come into being.

      Based on the above facts, ECM can be used to model the USDBTC data while accounting for the instability in the time series. From Table 13. it is apparent that both models have a similar log-

      likelihood, however the ADL has a significantly smaller MSFE, making it a better model for predicting Bitcoin price. Overall, as seen in Table 14., it is still the RSI, MACD Condition and Price Relative Close - EMA200 Price Diff which are the three indicators most statistically significant with prices. However, for the ECM model, Close.L1 and Accelerate.L1 become more significantly correlated with prices compared to the ADL model. Even more interestingly, we find that Price Relative ATR is statistically significant at the 1% level of significance in the ECM but is not statistically significant in the ADL. Hence, we decided to test it as part of the trading strategy in Section 5. to determine if can benefit trading performance.

      Interestingly, it is the volatility related indicators such as Acceleration and ATR that seem to demonstrate an increased statistical significance with the profitability of trades for the ECM. This may be because once the long-term trend has been removed from the data, it is the shorter timeframe volatility that accounts for most of the price action – and hence trade profitability.

      
      

      Table 13: Comparison of ADL and ECM
      Model	AR(1)-BH(1) ADL	AR(1)-BH(1) ECM
      Causal	False	False
      Trend	No Trend	No Trend
      Log Likelihood	3395.7	3409.735
      MSFEFPE	0.001392	0.002941

      * = significant at 10%, ** = significant at 5%, *** = significant at 1%

      
      

      Table 14. Comparison between ADL and ECM
      ADL-Lag1 Variable	Coefficient	P>|z|	ECM- Variable	Coefficient	P>|z|
      RSI.L0	0.0012	0.015**	RSI.L0	0.0012	0.015**
      RSI.L1	-0.0009	0.050*	RSI.L1	0.0003	0.133
      Price Relative Close-EMA200 Price Diff.L0	-0.1575	0.119	Price Relative Close-EMA200 Price Diff.L0	-0.1575	0.119
      Price Relative Close-EMA200 Price Diff.L1	0.1625	0.118	Price Relative Close-EMA200 Price Diff.L1	0.0051	0.900
      MACD Condition.L0	0.0254	0.000***	MACD Condition.L0	0.0254	0.018**
      MACD Condition.L1	0.0006	0.888	MACD Condition.L1	0.0259	0.000***
      Price Relative ATR.L1	-0.0037	0.377	Price Relative ATR.L1	0.0014	0.005***
      Close.L1	-6.549e-06	0.308	Close.L1	-7.357e-07	0.053*
      Acceleration.L1	0.0002	0.678	Acceleration.L1	-0.0002	0.071*

5. Evaluating Model Performance

   Having derived insights from the different models generated, we are now ready to test out different trading strategies. To summarize, the ADL model identified the RSI, MACD Condition and Price Relative Close-EMA200 Price Diff as statistically significant indicators, while the Error Correction Model (ECM) model identified Price Relative ATR as a significant regressor. In Section

   5.1. we will construct a strategy that uses these regressors to make trading decisions and compare the results against common trading strategies. In Section 5.2. the model will be applied to trading data on the hourly timeframe to determine if the strategy works for intraday trading. In Section

   5.3. we will adjust the holding times of the best performing strategy to determine if the profit can be improved by simply closing the trades more than 1 period after the trade is made. Lastly, in Section 5.4, we apply the best strategy, with the best holding time across different major cryptocurrency markets and compare the performance to determine if the strategy is feasible outside of Bitcoin.

   1. Trading Strategies

      Since the raw RSI values and MACD based trading strategy were identified as significant indicators, it is worthwhile to determine if the common RSI or MACD based trading strategy has any success. The results of the tests are shown in Annex – Strategy Performance. Each strategy is tested on two instruments from each type of market, and the average percentage profit per trade is captured in a chart. The RSI based trading strategy was found to perform poorly initially, barely profitable at 0.00045% profit per trade. However, with strategies that used additional trend and volatility indicators such as Trend, Price Relative Close-EMA200 Price Diff and Price Relative ATR, we found that the RSI trading strategy can be profitable, making an average of 4.49% returns per trade. Interestingly, setting a limit to the volatility in the market by using Price Relative ATR seemed to be able to filter out losing trades for the RSI strategy which on hindsight makes sense because when the price fluctuates wildly, it is possible to trigger RSI based trades even though there might not be a clear sign of a reversal.

      For the MACD trading strategy, the starting point greatly differed from RSI in that its profitability was clear (1.77% average per trade) across all instruments even with the basic strategy. By conducting similar augmentations from the RSI strategy to the MACD strategy, we were able to bring the average trade profitability to 6.71% per trade. Again, we noticed that controlling for the volatility was critical for increasing the quality of the trades, suggesting that reversal-based trading strategies can greatly benefit from a volatility filter. Based on the above findings, it is apparent that the regressors identified by the different models have greatly contributed to enhancing basic strategies that typically consider only the general trend and a signal.

   2. Trading Timeframes

      Table 15: Trading on Different Timeframes
      Trading Timeframe	BTC Daily Long Trades	BTC Daily Short Trades	BTC Hourly Long Trades	BTC Hourly Short Trades
      % Profit/Loss	2.58	-0.36	12.34	-0.62

      For a given trading strategy, different trading timeframes can have different success. In this section, we randomly sample a period of USDBTC hourly data and compare the trading performance of our current best strategy based on the MACD indicator, trend and volatility. The preliminary results in Table 15. showed that trading on the hourly timeframe strategy was significantly more profitable than the daily timeframe, with an average profitability of around 12% per long trade. The short trade performance on both timeframes were relatively similar, losing about 0.1% per trade on average. Having success at the lower timeframe indicates that the strategy has the potential to be highly profitable as it will be able to make more trades in each period of time.

      Additional research could be done to determine if the strategy still holds at

      the 1-minute, 15-minute and even the ticker level timeframe.

      Table 16. Mean Profit for Different Holding Times
      Holding Time (Days)	1	3	5	10	15	30
      Instrument	Mean % Profit
      BTC Long	2.37	3.36	4.07	7.00	9.37	14.21
      BTC Short	-0.42	-1.22	-1.91	-3.47	-5.18	-10.64
      DOGE Long	6.06	8.64	10.98	10.89	6.15	-13.26
      DOGE Short	3.8	3.53	3.34	-0.29	-0.59	-4.73
      Oil Long	2.16	2.13	2.47	2.63	1.12	0.36
      Oil Short	1.63	2.51	3.57	4.72	5.39	11.4
      Gold Long	1.3	1.29	1.06	0.57	0	-1.01
      Gold Short	0.85	0.93	1.09	0.77	1.52	2.06
      SP500 Long	0.3	-1.07	-1.16	-1.38	-3.55	-2.18
      SP500 Short	0.68	0.37	0.48	0.72	0.65	1.23
      STI Long	0.71	0.78	0.89	1.12	1.1	1.12
      STI Short	0.73	0.84	1.26	0.93	0.29	1.21
      All Instruments	1.68	1.84	2.18	2.02	1.36	-0.02

   3. Trade Holding Times

      Exiting a trade is just as important entering a trade. For the trading strategies employed thus far, the holding

      time has been set to one day after the trade is made, however, given that the market takes time to respond to signals, it may be possible that a longer holding time can result in increased profits, although it is equally true that once a trade is held for too long, the conditions of the market may have changed beyond the expectations of the trading strategy. In this section, we conduct a preliminary

      study on the effects of holding on to the trade for different periods of time and determine its effect on profits. Note that the model being used in this section is the MACD trading strategy with only considerations for Price Relative Close-EMA200 Price Diff. This is because the earlier model allows for more trades and across more instruments, allowing for a better general understanding of the

      effects of extending the holding times. Based on the results from Table 16., it is obvious that the optimal

      holding time for the trades may not be 1 day, in this instance, for the specific strategy, increasing the holding time to 5 days increases average profits by 29.7% per trade, which is substantial. This confirms the criticality of considering holding times when applying a trading strategy.

      
      

   4. Alternative Cryptocurrency Markets

      Cryptocurrencies outside of Bitcoin are potentially untouched markets for profit. The best performing strategy was applied to other major cryptocurrencies such as Dogecoin (DOGE), Binance Coin (BNB), Solana (SOL), Cardano (ADA), Ripple (XRP) and Ethereum (ETH). All the cryptocurrencies aside from SOL demonstrated profitability from the trading strategy, averaging 15.94% profit per trade on average across all markets. The dramatic increase in profits is due largely to the change in holding time to 3 days as the previous analysis suggested. When the exact same strategy is applied with a holding time of 1 day, the returns averaged at 8.34% per trade. Using the extended holding strategy, BNB was found to have an average of 7.86% profit per long trade and an average 6.21% profit per short trade. ADA returned an average of 6.38% per short trade. ETH demonstrated great potential for both long and short trades, returning 11.5% and 8.73% returns for each category respectively. Lastly, XRP demonstrated DOGE levels of profitability for long trades, at 83.0% per long trade – which is a surprising result because it is a relatively stable cryptocurrency market, while DOGE returns improved significantly to 40.5% per long trade after increasing the holding time. It was noted that the ADA long trades failed to trigger because the market did not trend upward strongly historically, hence potential trades did not meet the Price Relative Close-EMA200 Price Diff threshold to make trades. In the case of SOL, it only started trading in April 2020 resulting in much fewer data points as compared to the other cryptocurrencies, compounded with the requirement for 200 periods to pass before the 200EMA generates readings, SOL can be treated as an empty dataset.

      
      

6. Conclusion

In this research, we have progressively developed multiple ADL and ECM time series models to determine variables that are statistically significant to the profitability of trades. Through Section 3, the process of ensuring that the variables make sense in the context of the objective (trade profitability), and the process of exploring additional regressors (modified terms, non-linear terms, interaction terms) that could improve the model is critical in ensuring that regressors are properly represented. In this aspect, the price relativity of indicators played the biggest role by adjusting the indicators by the price at which the asset was worth at a given point in time. Following this, in Section 4, we had a pool of indicators which we repeatedly tested for statistical significance with (i) different models, (ii) different lags, (iii) different types of instruments, and considered (iv) the effects of events that tend to have a large impact on price. We found that hype, represented by Google Trends and major Bitcoin events were not statistically significant to the time series models despite the observation that these regressors seemed to influence on price. Most importantly, we found that RSI, MACD Condition, Price Relative Close-EMA200 Price Diff and Price Relative ATR were proven to be robustly significant across most of the above situations.

Using the knowledge gleaned from the above process, a few simple and logical trading strategies were developed using the chosen technical indicators in Section 5. Since each indicator was included with a specific intention from the start, the joint effects of these intentions allowed us to come up with trading strategies relatively quickly. The first strategy attempts to use RSI as a momentum indicator to make trades, it is important to note that while RSI had statistical significance to profit levels, the trading strategy based on RSI which is represented by RSI Condition was not statistically significant, indicating that it may not be functional on its own. Hence, we combined it with Trend to quickly determine if making trades that followed the trend were useful and found that the RSI strategy worked better when the trades were made following the overall trend. We then took this a step further by using Price Relative Close-EMA200 Price Diff to determine the strength of the trend, trading only when the trend is strong and this improved profitability further. Price Relative ATR, which is a volatility indicator was then used to filter out trades during periods when the price was volatile, this was found to have a further positive impact on trade returns. Having confirmed that the process of (i) confirming the strength of the trend and aligning trades with the direction of the trend and (ii) avoiding trades during highly volatile periods was beneficial, we applied the same methodology to improving the MACD Condition trading strategy and received similarly improved results.

Considering the above, time series models can be useful for identifying technical analysis indicators that affect trade profitability, and that these indicators can be used to construct profitable trading strategies. These strategies can then be further improved by adjusting basic trading parameters such as the timeframe on which the trades are made and the holding time of each trade. Note that because the RSI and MACD are momentum indicators used for swing trading during trend reversals, during market crashes, the strategy remains entirely feasible – this is important to note because certain trading strategies assume that market prices only go up as is the case of what we have seen for cryptocurrency in recent times.

Another important point to note is that while the usage of indicators that indicate trend strength and market volatility, appear to filter out poor trades, increasing trade quality and average returns, it also reduces the number of trades made. Finding the optimum point between trade quality and quantity is an aspect of this research that can be further developed. Additionally, the variance in success of a trading strategy between different categories of markets – and even within instruments belonging to a same market category is significant. It appears that the tendency for strong trends to occur in cryptocurrency markets is larger than in equities (SP500 and STI) and commodities (Oil and Gold) hence we see the reversal compounded with strong trend strategy conducting a higher quantity of trades at a higher quality when in the cryptocurrency market. This insight points towards the requirement for a careful selection of items in a trading portfolio that are specifically catered to a trading strategy. In sum, the ground has already been laid for demonstrating the effectiveness of using econometric analysis to develop a trading strategy based on technical analysis, and we are excited to see these strategies applied under real market conditions.

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Annex A – Popular Technical Indicators (Formula and Application)

Popular Technical Indicators (Formula and Application)
Name	Formula	Application
Average True Range (ATR)		Measures the daily volatility of an asset. The indicator does not indicate the price direction; rather it is used primarily to measure volatility caused by gaps and limit up or down moves.
Bollinger Band (BB)		The closer prices move to the upper band, the more overbought the market, and the closer the prices move to the lower band, the more oversold the market.
Exponential Moving Average (EMA)		The 200-day EMA is used as an indicator for long-term trends. When a stock price crosses its 200-day moving average, it is a technical signal that a trend reversal has occurred.
Moving Average Convergence Divergence (MACD)	Signal Line = MACD 9-Period EMA	Traders may buy the instrument when the MACD crosses above its signal line and sell the security when the MACD crosses below the signal line.
Relative Strength Index (RSI)		RSI values of 70 or above indicate an instrument is overvalued and primed for a trend reversal. An RSI reading of 30 or below indicates an undervalued condition.

Annex B – Robustness Checks

Effect of Google Trends

The term "herd mentality" [6] refers to a phenomenon where people join groups and follow the actions of others under the assumption that other individuals have already done their research. Herd instincts are common in all aspects of society, even within the financial sectors, where investors follow what they perceive other investors rather than rely on their own analysis. Researchers have conducted empirical studies [6,7,8,9] to demonstrate that the investors may have a "herd mentality" when making investment decisions, i.e., other investors' actions may affect one investor's own decision. For example, if one investor finds that many people (e.g., their friends) on the Internet are discussing cryptocurrency, they are more likely to start investing in cryptocurrency.

In the current society where social media is so well-developed, investors are not only affected by people around them (e.g., friends or colleagues), they all receive instant information from the Internet or social media. Suppose investors see that people on the Internet are all talking about Bitcoin. In that case, they may not be able to resist the temptation to search Bitcoin and seek potential investment opportunities. Google is currently one of the most widely used search engines in most of the countries in the world. Google trends are some aggregated data showing that how frequently Google users search certain keywords. Such data can be used to understand and predict financial [10] and even public health events [11]. For example, researchers use the abnormal increase of Google search trends of keywords like "headache", "cough", etc., to estimate whether Covid-19 has been spread in certain regions [1].

In this section, we plan to analyze whether Google Trends data can help our model perform the changes in Bitcoin price. The following two intuitions motivate us to perform such an analysis. On the one hand, Google Trends, to some extent, can reflect the new investors into the cryptocurrency market. A surge in the frequency of a cryptocurrency-related keyword being searched can mean that more investors are paying attention to it, and as a result, they may eventually become investors, which leads to a rise in the Bitcoin price. On the other side, Google Trends may reflect some important evens in cryptocurrency investments. For example, big companies announce that they accept Bitcoin for payment or the reward for mining bitcoin transactions is cut in half (Bitcoin halving events).

Figure 2 The trends of how frequently the keyword "bitcoin" is searched in the past five years. The data is collected worldwide and normalized.

Figure 3 The trends of how frequently the keyword "cryptocurrency" is searched in the past five years. The data is collected worldwide and normalized.

Figure 4 The trends of how frequently the keyword "dogecoin" is searched in the past five years. The data is collected worldwide and normalized.

We first introduce how we collect and process the Google Trends data on cryptocurrency-related keywords. Figure 2 illustrates the trends depicting how frequently the keyword “Bitcoin”

has been searched in the past five years (worldwide search data), and Figure 3 shows the trends depicting how frequently the keyword “cryptocurrency” is searched in the past five years (worldwide search data). As we can observe from the two figures, the two trends are quite similar to each other. However, we also collected the search data for “dogecoin”, which was previously a non-mainstream cryptocurrency but has soared in the recent year. We can observe that its search trend is greatly different from the trends of either “Bitcoin” or “cryptocurrency”. Since we investigate the trends in a period of 5 years, we use the Google trends data for more commonly used and representative keywords like “Bitcoin”.

After downloading Google Trends data as a CSV file, we perform some pre-processing. More specifically, when we request data for a more extended period (e.g., one year or longer), Google only returns weekly data. It uses the average search data for each week. We also need to point out that the search trends data is normalized. We do not have the exact times of a Google being searched per week, but we can see the relative trends between two-week data. So sample data is shown in Table 1. To make the data can be used in our previously built model. We expand these weekly data to daily data by assigning the single weekly search data to each day in that week.

Table 1 Sample data pints from the Google Trends data.

After pre-processing these weekly data into daily data, we add the Google Trends data as an additional independent variable, and run the model again. We display the statistical results related to the Google Trend variable in the following table:

As we can observe from this table, the significance for both trend-L0 and trend-L1 is not high, which means that the Google Trend data on “Bitcoin” does not contribute to making a better model. Based on the analysis of using Google Trend as an additional independent variable, we make the following suggestions to the investors: There is no strong evidence suggesting the strong correlation between Google Trend data and the Bitcoin price change. So we suggest the users not follow the trend (i.e., avoid herd mentality) to make decisions.

Effect of Significant Events

Since Bitcoin was developed in 2009, it has gone through several bull runs – in 2011, 2013, 2017 and, in 2021, is currently going through another. The meteoric increase in prices during Bitcoin’s bull runs have garnered Bitcoin a huge amount of interest from the public, and have most commonly been attributed to an upgrade of Bitcoin’s technology, and the halving of rewards for Bitcoin miners.

From the table below, it can clearly be seen that there is some sort of correlation between Bitcoin’s bull runs and the halving dates/bitcoin upgrade.

Using the 2017 Bitcoin upgrade (SegWit) as an example, we will use this event as control variables to determine its impact on the price of Bitcoin, as well as Bitcoin’s future prices on the current price, as described in section 3.

Firstly, using a dummy variable to run ARDL, the results show that the event is not statistically significance in terms of the regression of future prices on current price. Additionally, running ARDL on different time frames show that the event becomes even less independent as time frame increases.

Next, we run ARDL on the Bitcoin Close price to the SegWit event and on USD. One would expect the such a major event to have an effect on the price Bitcoin. However, ARDL results also show that the dummy variable of this event has no statistical significance.

This would be because adding a dummy variable changes the coefficient of regressor before and after the event. Upon analysis of the Bitcoin price chart, it can be seen that the price does not

increase outright due to the event. Rather, the trend that the price is following changes. (i.e. the gradient of the line) To measure the impact of the event on the trend, the Chow test, which is used to measure the effects of structural breaks on time-series data, is used.

Performing the Chow test on Bitcoin’s Close price to USD and the SegWit event dummy variable, yields a Chow score of 0.053 and a p-value of 1.68e-12, which is statistically significant. This also matches with what is seen on the BTC-USD chart, where trend in Bitcoin prices after SegWit event was that the price increased at a much faster rate than prices before the event. Performing the Chow test on Bitcoin’s Future Price (1 day later) to Close price and the SegWit event yields a p-value of 0.00029, which is statistically significant. However, Performing the Chow test on Bitcoin’s future Price of 3 days of more yields a p-value that is not statistically significant.

This shows that there is a significant trend change in Bitcoin’s 1 day Future Prices as compared to Close price upon the SegWit event occurring, however, the trend change becomes insignificant as a result of the structural break if the time range of future prices were to be increased.

Running the Chow test on the 2016 Halving produces similar results, with a statistically significant p-value of 0.0035 for BTC-USD price, and 1.32e-18 for Future Price 1 to Close price. Similarly, using the dummy variable directly for ARDL regression, produces statistically insignificant results.

Annex C – Charts and Tables

Basic RSI Trading Strategy (average 0.0045% per trade across all instruments)

Basic RSI Trading Strategy with Trend (average +0.157% per trade)

RSI Trading Strategy with Price Diff between Price and EMA200 (average 2.53% per trade)

RSI Trading Strategy with Price Diff between Price and EMA200 (>0.1) and Price Relative ATR (<10) (average 4.49% per trade)

MACD Trading Strategy (average 1.77% per trade)

MACD Trading Strategy with Trend (average 2.01% per trade)

MACD Trading Strategy with Price Diff between Price and EMA200 (> 0.2) (average 5.15% per trade)

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MACD Trading Strategy with Price Diff between Price and EMA200 (>0.5) and Price Relative ATR (<30) (average 6.70% per trade)

BTC Hourly vs Daily Timeframe Trade Performance

Holding Time = 1 Day (Average +1.68% per trade)

Holding Time = 3 Days (Average +1.84% per trade)

Holding Time = 5 Days (Average +2.17% per trade)

Holding Time = 10 Days (Average +2.02% per trade)

Holding Time = 15 Days (Average +1.35% per trade)

Holding Time = 30 Days (Average -0.018% per trade)

coef std err

z P>|z| [0.025 0.975]

const -0.0554 0.017 -3.347 0.001 -0.088 -0.023

future_price1 % P/L.L1 -0.2639 0.070 -3.752 0.000 -0.402 -0.126

future_price1 % P/L.L2 -0.0950 0.071 -1.341 0.180 -0.234 0.044

future_price1 % P/L.L3 -0.0558 0.071 -0.789 0.430 -0.194 0.083

future_price1 % P/L.L4 -0.1137 0.071 -1.605 0.109 -0.253 0.025

future_price1 % P/L.L5 -0.1691 0.071 -2.383 0.017 -0.308 -0.030

Model with Lag = 8

const -0.0516 0.015 -3.436 0.001 -0.081 -0.022

future_price1 % P/L.L1 -0.2743 0.070 -3.910 0.000 -0.412 -0.137

future_price1 % P/L.L2 -0.0528 0.071 -0.743 0.458 -0.192 0.087

future_price1 % P/L.L3 -0.0560 0.071 -0.786 0.432 -0.196 0.084

future_price1 % P/L.L4 -0.0844 0.071 -1.188 0.235 -0.224 0.055

future_price1 % P/L.L5 -0.1589 0.071 -2.241 0.025 -0.298 -0.020